ABSTRACT A closed-form analytical solution to rheological phenomena is obtained based on Hoek-Brown (HB) yield criterion and the generalized Bingham model. Once the circular tunnel is excavated, an initial plastic region is formed. When the total stresses fulfil the yield condition, the initial plastic region steps into the viscoplastic region, in which the displacement develops with time. The one-dimensional constitutive equation of the generalized Bingham model is transformed into a three-dimensional expression in polar coordinates by combining the plane strain condition. With the help of equilibrium differential equation, geometric equation and boundary condition, the stress and displacement in the initial plastic region can be expressed. At the moment of t, the stresses and displacements are described similar to the solutions of the elasto-plastic state. The stresses, strains and displacements after transformation can be expressed in the viscoplastic region. The proposed solution was verified by the closed-form solution of circular tunnels in elastic-brittle-plastic rock mass.

Abstract This paper deals with a deep circular tunnel excavated in infinite homogeneous and isotropic elasto-viscoplastic rock mass subjected to a hydrostatic initial stresses. The tunnel is divided into the initial plastic, viscoplastic, and elastic zones. By combining the generalized Bingham model with Mohr-Coulomb yield criteria, analytical solutions of the circular tunnel are derived with the consideration of non-associated flow rule and elasto-viscoplasticity. The initial plastic zone is defined as the instantaneous change of rock mass excavation. Based on the initial plastic zone, the stresses in viscoplastic zone are transferred to the deep surrounding rock with time due to the initial earth stresses. The results are compared with the elastic-brittle solution at static conditions, and the solutions of this paper are validated. Moreover, the presented results shows that the stress and displacement of the surrounding rock varies with time, and the solutions can be obtained at different instants of time.

ABSTRACT This paper deals with a spherical cavity excavated in infinite homogeneous and isotropic strain-softening rock mass subjected to a hydrostatic initial stresses. By simplifying the strain-softening process of the post-failure region as a Multi-step Brittle-Plastic model (MBPM), analytical solutions of the spherical cavity are derived with the consideration of the deterioration of elastic parameters. Meanwhile, critical deterioration conditions of elastic parameters are established theoretically. Both Mohr-Coulomb (M-C) and Hoek-Brown (H-B) criteria are included in the analysis. The results are compared with those obtained by former numerical methods, and the solutions are validated. Moreover, the presented results show that deteriorated elastic parameters for post-failure rock mass only has a little influence on stresses, softening radius and residual radius, but influences the deformation significantly.

The rolled AZ31 Mg alloy sheets were processed by multi-pass bending (MPB) process at room temperature and followed by annealing treatment. Mechanical properties of the as-received and MPB sheets in annealed conditions were examined based on the concurrent microstructure and texture evolution. The results show that the room temperature ductility of the Mg sheets was improved by multi-pass bending process. Moreover, the (0002) basal texture was drastically weakened. Enhanced the ambient mechanical properties, such as lower yield strength and larger uniform elongation, were fabricated by MPB path due to the weak basal texture. The microstructure and mechanical responses were characterized and discussed.